In a joint statement, the top Democrats in Congress, Senator Chuck Schumer of New York and Representative Nancy Pelosi of California, said Mr. Trump had “apparently decided to punish the American people for his inability to improve our health care system.”

“It is a spiteful act of vast, pointless sabotage leveled at working families and the middle class in every corner of America,” they said. “Make no mistake about it, Trump will try to blame the Affordable Care Act, but this will fall on his back and he will pay the price for it.”

Lawmakers from both parties have urged the president to continue the payments. Mr. Trump had raised the possibility of eliminating the subsidies at a White House meeting with Republican senators several months ago. At the time, one senator told him that the Republican Party would effectively “own health care” as a political issue if the president did so.

“Cutting health care subsidies will mean more uninsured in my district,” Representative Ileana Ros-Lehtinen, Republican of Florida, wrote on Twitter late Thursday. She added that Mr. Trump “promised more access, affordable coverage. This does opposite.”

But Speaker Paul D. Ryan, Republican of Wisconsin, praised Mr. Trump’s decision and said the Obama administration had usurped the authority of Congress by paying the subsidies. “Under our Constitution,” Mr. Ryan said, “the power of the purse belongs to Congress, not the executive branch.”

The future of the payments has been in doubt because of a lawsuit filed in 2014 by House Republicans, who said the Obama administration was paying the subsidies illegally. Judge Rosemary M. Collyer of the United States District Court in Washington agreed, finding that Congress had never appropriated money for the cost-sharing subsidies.

The Obama administration appealed the ruling. The Trump administration has continued the payments from month to month, even though Mr. Trump has made clear that he detests the payments and sees them as a bailout for insurance companies.

This summer, a group of states, including New York and California, was allowed to intervene in the court case over the subsidies. The New York attorney general, Eric T. Schneiderman, said on Thursday night that the coalition of states “stands ready to sue” if Mr. Trump cut off the subsidies.

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Mr. Trump’s decision to stop the subsidy payments puts pressure on Congress to provide money for them in a spending bill.

Senator Lamar Alexander, Republican of Tennessee and the chairman of the Senate health committee, and Senator Patty Murray of Washington, the senior Democrat on the panel, have been trying to work out a bipartisan deal that would continue the subsidy payments while making it easier for states to obtain waivers from some requirements of the Affordable Care Act. White House officials have sent mixed signals about whether Mr. Trump was open to such a deal.

The decision to end subsidies came on the heels of Mr. Trump’s executive order, which he signed earlier Thursday.

With an 1,100-word directive to federal agencies, the president laid the groundwork for an expanding array of health insurance products, mainly less comprehensive plans offered through associations of small employers and greater use of short-term medical coverage.

Most of the changes will not occur until federal agencies write and adopt regulations implementing them. The process, which includes a period for public comments, could take months. That means the order will probably not affect insurance coverage next year, but could lead to major changes in 2019.

“With these actions,” Mr. Trump said at a White House ceremony, “we are moving toward lower costs and more options in the health care market, and taking crucial steps toward saving the American people from the nightmare of Obamacare.”

“This is going to be something that millions and millions of people will be signing up for,” the president predicted, “and they’re going to be very happy.”

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But many patients, doctors, hospital executives and state insurance regulators were not so happy. They said the changes envisioned by Mr. Trump could raise costs for sick people, increase sales of bare-bones insurance and add uncertainty to wobbly health insurance markets.

Chris Hansen, the president of the lobbying arm of the American Cancer Society, said the order “could leave millions of cancer patients and survivors unable to access meaningful coverage.”

In a statement from six physician groups, including the American Academy of Family Physicians, the doctors predicted that “allowing insurers to sell narrow, low-cost health plans likely will cause significant economic harm to women and older, sicker Americans who stand to face higher-cost and fewer insurance options.”

While many health insurers remained silent about the executive order, some voiced concern that it could destabilize the market. The Trump proposal “would draw younger and healthier people away from the exchanges and drive additional plans out of the market,” warned Ceci Connolly, the chief executive of the Alliance of Community Health Plans.

Administration officials said they had not yet decided which federal and state rules would apply to the new products.

The Affordable Care Act has expanded private insurance to millions of people through the creation of marketplaces, also known as exchanges, where people can purchase plans, in many cases using government subsidies to offset the cost. It also required that plans offered on the exchanges include a specific set of benefits, including hospital care, maternity care and mental health services, and it prohibited insurers from denying coverage to people with pre-existing medical conditions.

The executive order’s quickest effect on the marketplaces would be the potential expansion of short-term plans, which are exempt from Affordable Care Act requirements. Many health policy experts worry that if large numbers of healthy people move into such plans, it would drive up premiums for those left in Affordable Care Act plans because the risk pool would have sicker people.

“If the short-term plans are able to siphon off the healthiest people, then the more highly regulated marketplaces may not be sustainable,” said Larry Levitt, a senior vice president for the Kaiser Family Foundation. “These plans follow no rules.”

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Mr. Trump’s order would also eventually make it easier for small businesses to band together and buy insurance through entities known as association health plans, which could be created by business and professional groups. A White House official said these health plans “could potentially allow American employers to form groups across state lines” — a goal championed by Mr. Trump and many other Republicans — allowing more options and the formation of larger risk pools.

The White House said that a broader interpretation of federal law — the Employee Retirement Income Security Act of 1974 — “could potentially allow employers in the same line of business anywhere in the country to join together to offer health care coverage to their employees.”

The order won applause from potential sponsors of association health plans, including the National Federation of Independent Business, the National Restaurant Association, the U.S. Chamber of Commerce and Associated Builders and Contractors, a trade group for the construction industry.

The White House released a document saying that some consumer protections would remain in place for association plans. But state officials pointed out that an association health plan can set different rates for different employers, so that a company with older, sicker workers might have to pay much more than a firm with young, healthy employees.

“Two employers in an association can be charged very different rates, based on the medical claims filed by their employees,” said Mike Kreidler, the state insurance commissioner in Washington.

Mr. Trump’s order followed the pattern of previous policy shifts that originated with similar directives to agencies to come up with new rules.

Within hours of his inauguration in January, he ordered federal agencies to find ways to waive or defer provisions of the Affordable Care Act that might burden consumers, insurers or health care providers. In May, he directed officials to help employers with religious objections to the federal mandate for insurance coverage of contraception.

Both of those orders were followed up with specific, substantive regulations that rolled back Mr. Obama’s policies.

In battles over the Affordable Care Act this year, Mr. Trump and Senate Republicans said they wanted to give state officials vast new power to regulate insurance because state officials were wiser than federal officials and better understood local needs. But under Thursday’s order, the federal government could pre-empt many state insurance rules, a prospect that alarms state insurance regulators.